Problem
Dr. Hoffman has created a new test to measure self-esteem. It consists of ten items and each item is rated 1-Disagree, 2-Neutral, or 3-Agree by the test taker. A sample item is "I am able to do many things well." On every item, "Agree" indicates higher self-esteem. The total score is determined but adding up item scores, and so it can range from 10 to 30.
She administers the test to large samples that are representative of the US population and creates the following norms:
Mean Std Dev
Females, 18-39 15.0 2.5
Males, 18-39 18.0 2.8
Females, 40 and older 11.5 2.5
Males, 40 and older 12.0 2.6
Assuming that Dr. Hoffman's test is a valid measure of self-esteem, what do these norms tell you about the relationship between gender, age and self-esteem? Carol, a 50-year-old woman, obtains a score of 14. How would you interpret this score?